Two men who have shared a particular sexual partner consecutively, although not necessarily in quick succession. The essence is, your Milk Brother was the last person to have slept with this particular partner before you did. (Like blood brothers have shared blood, milk brothers have shared milk, at least symbolically.)
Guy at Party: "Why does Javier's girlfriend get all tense, but also kinda flirty whenever Claude is around?"
Guy 2: "She used to bang Claude. In fact, Claude and Javier are Milk Brothers"
Male friends who have shared sexual exploits (ie. having sexual intercourse with the same woman at the same time.)
Carlos & Diego are milk brothers; when they go out to hook up, they often bring back one chick and both do her.
From the Spanish "Hermanos de leche". This referes to two men who have have had sexual relations with the same woman.
The phrase originally referred to unrelated children who were breastfed by the same woman, symbolically becoming brothers, by sharing in this motherly attention.
The children became symbolic brothers by suckling at the same breast, hence the men become symbolic brothers through a similar, but less nutritious, action.
"Me and Jose both banged Estefany, so now we're milk brothers."
"Maria is such a slut, half the guys in town are milk brothers now."